a friend who studies pure mathematics ask me to think about this problem: suppose that there is an algorithm named X that have 2 inputs: A and a_1...a_n, 'A' stands for an arbitary

algorithm and 'a_1..a_n' are inputs of A. X recieves A and its inputs and returns true if A with a_1..a_n couold

be terminated, and false if A with a_1..a_n inputs fall into infty loop (never ends). like this:

A(n):
   while(n<5):
      write "I'm immortal!"

and result of X(A,6) is true and X(A,2) is false.

so what is the result of X(X,X)?

...and do you know who introduced this problem first time?